This invention relates to devices for performing filtering functions on signals using digital filtering techniques, and, more particularly, to a digital filter capable of operating with consistency over a wide range of cutoff frequencies and spectral shapes.
In many signal processing areas, a filter whose cutoff frequency and rolloff characteristics can be programmed with high resolution is desired. Common filtering tasks in communication systems include the minimizing of Inter-Symbol Interference (ISI) using Nyquist filters, the use of a matched filter (a filter with characteristics matched or complementary to characteristics of the signal applied to the communication channel) at the receiving end of a channel to maximize the receiver signal-to-noise ratio (SNR), and the attenuation of out-of-band interference. Changeable rolloff characteristics and frequency cutoff points allow the communication systems to operate over a variety of data rates and channel conditions.
The tasks of filtering and sampling analog signals can be done with various combinations of analog and digital filtering. A common technique is use of a fixed analog filter with the desired frequency characteristics followed by a sampler on the analog filter output sampling at the desired sampling rate. Cost, flexibility, and performance considerations suggest the replacement of analog systems with systems or devices employing digital signal processing (DSP) techniques.
Many systems require the capability of selectively varying sampling rate and bandwidth. A programmable sampling rate as well as a programmable bandwidth can be done in the analog domain or more preferably, in the digital domain. A very common sampling approach is to sample the signal at a rate of four times the bandwidth of the required filter.
Filter realizations involving the use of an analog filter having a variable bandwidth are complex and expensive. Other filter realizations, such as the use of several fixed analog filters and a selection switch to select among them, lack the flexibility of frequency selection and yet require time-consuming and often difficult alignment in the manufacturing process. Digital filters which employ a variable bandwidth using fixed-rate sampling lose the constant factor between the output bandwidth and the output sampling rate, and therefore there is a need to convert the output to an analog waveform and then to re-sample the output at the desired rate. They also can be expensive to implement for very wide ranges of frequency programmability.
The use of half-band digital filters has been proposed for efficient implementations of decimation or interpolation by powers of two. See for example Bellanger et al., "Interpolation, extrapolation, and reduction of computation speed in digital filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-22, pp. 231-235, August, 1974. Also suggested have been an optimized multistage process for sampling rate reduction or increase. See R. R. Shively, "On multistage FIR filters with decimation," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-23, pp. 353-357, August, 1975; and R. E. Crochiere and L. R. Rabiner, "Optimum FIR digital filter implementations for decimation, interpolation, and narrow-band filtering," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-23, pp. 444-456, October, 1975.
Half-band digital filters can be realized with a small computational burden as polyphase recursive all-pass subfilters with phase shifts selected to add constructively in the passband and destructively in the stopband. See for example P. A. Regaila, et al., "The digital all-pass filter: a versatile signal processing building block," Proc. IEEE, vol. 76, No. 1, January, 1988.
The problem with these digital implementations is that only a small number of sampling rates can be realized.
What is needed is a versatile filter realization with a variable sample clock which minimizes computation burden, expense, and signal quality degradation, while maximizing flexibility.